In this day of clickbait titles, studies that are not reproducible, and suspect motivation for studies, the idea that we can calculate the total number of birds with an error rate of less than 30%, including the fact that some data is 50 years old, doesn't pass my smell test.
I would prefer waiting for accurate data rather than panic over yet another headline that is not anchored in actual science and facts. For example, did they try to count the number of birds at the same time of the year both times? Do some birds have different multi-year migratory patterns leading to them being in different parts of the world? Did they try counting the birds twice using the same techniques but two different teams, and then compare the numbers?
There are too many ways this calculation could fail for me to be trust this data point.